Algebraic Number/Examples/Cube Root of 6

Example of Algebraic Number

$\sqrt [3] 6$ is an algebraic number.

Proof

\(\ds x\)

\(=\)

\(\ds \sqrt [3] 6\)

\(\ds \leadsto \ \ \)

\(\ds x^3\)

\(=\)

\(\ds 6\)

\(\ds \leadsto \ \ \)

\(\ds x^3 - 6\)

\(=\)

\(\ds 0\)

Hence the result by definition of algebraic number.

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): algebraic number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): algebraic number